 reserve L for Lattice;
 reserve I,P for non empty ClosedSubset of L;
reserve L for lower-bounded pseudocomplemented Lattice;

theorem Th6:
  for a, b being Element of L holds a [= b implies b* [= a*
  proof
    let a, b be Element of L;
    assume a [= b; then
a1: a "/\" b = a by LATTICES:4;
a2: a* is_a_pseudocomplement_of a by def3;
    a "/\" (b*) = (b* "/\" b) "/\" a by a1,LATTICES:def 7
    .= Bottom L "/\" a by ThD .= Bottom L;
    hence b* [= a* by a2;
  end;
